The energy level and wave functions were analyzed using an efficient preconditioned inexact spectral transform method. An extremely efficient preconditioner consisting of two components was developed. The components comprised of removing off-diagonal coupling near the energies and off-diagonal elements of minimized Hamiltonian matrix. The new preconditioner were found capable to calculate high-lying vibrational states with orders of magnitude fewer matrix-vector products. Preconditioners also accelerated the photodissociation cross sections and rate constants.